cosine load distribution

[ABV97]

Hi,
I am deaing with a beam having a reaction moment in the middle of the beam. Beam is simply supported. Assumption is that the load have a cosine distribution with a running load w = (pi*2 x M)/L*2 x 2 [lb/in].
Does anybody know where can I find more information about cosine load distribution, confirming that formula?

Thank you in advance all,

 

[rb1957]

do you have a reaction moment in the middle of the beam (ie a point moment) or a distributed load (capable of both tension and compression) ? i visualise the latter as like a tube over your beam, moment being applied to the tube, the tube applying load to both sides of the beam, the couple is applied as contact forces).

FWIW, i'd use a linear distribution to apply moment.

also you "cosine" definition is incomplete, you need the phase angle ... is the peak load at the middle (that sounds odd, but that's what i think of as a cosine dist'n, modelling the 1st and 4th quadrants) or is minimium load at the middle (sounds more realistic for a moment loading, but sounds more like a sine dist'n, modelling the 1st and 4th quadrants; of course exactly the same as cosine 1st and 2nd quadrants) ?

Quando Omni Flunkus Moritati

 

[ABV97]

Thank you rb1957, I am trying to absorb what you have said, and I just got another answer for the cosine distribution in the Mechanicak section (I promise, I won't post it twice anymore - I am new to the forum) which make sense!